Home
Class 12
MATHS
In any triangle A B C , prove that: a^3c...

In any triangle `A B C ,` prove that: `a^3cos(B-C)+b^3cos(C-A)+c^3cos(A-B)=3a b c`

A

3abc

B

2abc

C

abc

D

5abc

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRY

    BITSAT GUIDE|Exercise BITSAT Archives|41 Videos
  • THREE DIMENSIONAL GEOMETRY

    BITSAT GUIDE|Exercise BITSAT ARCHIVES |11 Videos
  • VECTOR ALGEBRA

    BITSAT GUIDE|Exercise BITSAT Archives|21 Videos

Similar Questions

Explore conceptually related problems

In any triangle ABC, prove that: a^(3)cos(B-C)+b^(3)cos(C-A)+c^(3)cos(A-B)=3abc

In Delta ABC, prove that a^(3)cos(B-C)+b^(3)cos(C-A)+c^(3)cos(A-B)=3abc

Prove that in /_ABC,a^(3)cos(B-C)+b^(3)cos(C-A)+c^(3)cos(A-B)=3abc

In any triangle ABC,prove that sin^(3)A cos(B-C)+sin^(3)B cos(C-A)+sin^(3)C cos(A-B)=3sin A sin B sin C

In any triangle,prove that b cos B+c cos C=a cos(B-C)

In a ABC, prove that sin^(3)A cos(B-C)+sin^(3)B cos(C-A)+sin^(3)C cos(A-B)=3s in As in Bs in

For any triangle ABC,prove that a(b cos C-c cos B)=b^(2)-c^(2)

For any triangle ABC, prove that (b+c)cos(B+C)/(2)=a cos(B-C)/(2)

BITSAT GUIDE-TRIGONOMETRY-BITSAT Archives
  1. In any triangle A B C , prove that: a^3cos(B-C)+b^3cos(C-A)+c^3cos(A-B...

    Text Solution

    |

  2. Number of roots of the equation |sinxcosx| +sqrt(2+t a n^2x+cot^2x)=sq...

    Text Solution

    |

  3. The greatest and least values of (sin^(-1)x)^(2) + (cos^(-1)x)^(2) are...

    Text Solution

    |

  4. Find the number of solutions of cos x =|1+ sin x |, 0 le x le 3 pi

    Text Solution

    |

  5. The vaue of the expression sin [cot^(-1){cos (tan^(-1))}] is

    Text Solution

    |

  6. An object is observed from the points A, B and C lying in a horizontal...

    Text Solution

    |

  7. If tan 20^(@) =lamda, then (tan 160^(@) -tan 110^(@))/(1+ (tan 160^(@)...

    Text Solution

    |

  8. The angles of a triangle are in AP and the least angle is 30^(@). What...

    Text Solution

    |

  9. If A+B+C=90^(@)," then "(cot A+ cot B+ cot C)/(cot A cot B cot C) is e...

    Text Solution

    |

  10. In Delta ABC, if a=2, b=3 and sin A =(2)/(3). Then, cos C is equal to

    Text Solution

    |

  11. If 4 sin^(-1) x + cos^(-1) x= pi, then x is equal to

    Text Solution

    |

  12. If tan theta =(1)/(2) and tan phi =(1)/(3), then the value of theta + ...

    Text Solution

    |

  13. If sin theta =(1)/(2) and tan theta =(1)/(sqrt(3)), AA n in l, then mo...

    Text Solution

    |

  14. The function sin x + cos x is maximum, when x is equal to

    Text Solution

    |

  15. Principal value of sin^(-1). (-(sqrt(3))/(2))is

    Text Solution

    |

  16. If angles A,B and C are in AP, then (a+c)/(b) is equal to

    Text Solution

    |

  17. (1+cos.(pi)/(8))(1+cos.(3pi)/(8))(1+cos.(5pi)/(8))(1+cos.(7pi)/(8)) is...

    Text Solution

    |

  18. The solution of the equation sectheta-cosectheta=(4)/(3) is

    Text Solution

    |

  19. What is the minimum value of 9 tan ^(2) theta + 4 cot ^(2) theta ?

    Text Solution

    |

  20. If a le sin^(-1) x+cos^(-1)x+tan^(-1) x le b, then

    Text Solution

    |

  21. If sin^(-1)x+sin^(-1) y=(2pi)/3 and cos^(-1)x-cos^(-1) y= pi/3 ," then...

    Text Solution

    |